The constant, \(A\) , hereafter the metric constant, may be thought of as a normalization (see Sec. REF ). The QFI matrix can be decomposed into a real, symmetric, Riemannian metric \(g\)  [1]}, and an anti-symmetric symplectic tensor \(\Gamma \)  (the Berry curvature [2]}),
\(Q_{\mu \nu } = g_{\mu \nu } + i\Gamma _{\mu \nu },\) 
